MCQ
If $\text{x}=4-\sqrt{15},$ then the value of $(\text{x}+\frac{1}{\text{x}})$ is:
- A$7$
- B$6$
- ✓$8$
- D$10$
✓
Answer
Correct option: C.
$8$
$\text{x}+\frac{1}{\text{x}}=\frac{\text{x}^2+1}{\text{x}}$
Now, Put $\text{x}=4-\sqrt{15}$
$\Rightarrow\frac{(4-\sqrt{15})^2+1}{4-\sqrt{15}}$
$\Rightarrow\frac{16+15-8\sqrt{15}+1}{4-\sqrt{15}}$
$\Rightarrow\frac{32-8\sqrt{15}}{4-\sqrt{15}}$
$\Rightarrow8$
Now, Put $\text{x}=4-\sqrt{15}$
$\Rightarrow\frac{(4-\sqrt{15})^2+1}{4-\sqrt{15}}$
$\Rightarrow\frac{16+15-8\sqrt{15}+1}{4-\sqrt{15}}$
$\Rightarrow\frac{32-8\sqrt{15}}{4-\sqrt{15}}$
$\Rightarrow8$
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